Abstract
The analysis of genomic data makes it possible to characterize the demographic processes that shaped the genetic diversity of populations. State-of-the-art in data analyses of genomic data is increasingly simulation-based, but disadvantages of simulation-based procedures include that they are highly computer intensive, often depend on the choice of summary statistics, and a rather indirect procedure for understanding key properties of both the data and the model. As an alternative to simulations, I will outline an emerging mathematical framework for genetic diversity based on matrix-exponential distributions. The main idea is that the ancestral process of a genetic sample can be described using a generalization of the exponential distribution called a phase-type distribution. Phase-type distributions have been used with great success in the actuarial sciences and in queuing theory, but the distribution is also well suited for the ancestral process. I will describe recent results of using phase-type distributions in population genetics, and discuss the latest progress and future plans for the framework.


Asger Hobolth is a Professor in the Department of Mathematics at Aarhus University.

https://pure.au.dk/portal/en/persons/asger-hobolth(8d387f4e-86e9-4405-a50d-1e5a6efd97d8).html